The hosts marked Mirko Slomka's first game at the helm in style and Calhanoglu put the icing on the cake when he lined up a free-kick 50 yards from goal as the game entered stoppage time.
With the Dortmund players seemingly expecting the Turk to play a simple short pass, they decided against forming a wall and Calhanoglu duly sent a swerving, dipping effort beyond Roman Weidenfeller and into the top left-hand corner of the goal.
It was an incredible strike to seal a surprise victory for Hamburg, who parted company with Bert van Marwijk last week after a run of eight straight defeats in all competitions.
But Calhanoglu insisted that it was the sort of finish that he tries all the time on the training pitch.
"I hit the free-kick the same way I do in training all the time," he told Bundesliga Live.
"I'm delighted that I pulled it off!
"It's an absolute dream to be able to beat Dortmund. We're in a much better place now."
Slomka, meanwhile, was similarly nonchalant about the goal.
"I've seen him do this before in training," he said.
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